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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

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[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
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April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
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[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
J
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Unsolved NT, 3rd time posting
GreekIdiot   11
N a few seconds ago by GreekIdiot
Source: own
Solve $5^x-2^y=z^3$ where $x,y,z \in \mathbb Z$
Hint
11 replies
GreekIdiot
Mar 26, 2025
GreekIdiot
a few seconds ago
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Bashing??
John_Mgr   2
N 4 minutes ago by GreekIdiot
I have learned little about what bashing mean as i am planning to start geo, feels like its less effort required and doesnt need much knowledge about the synthetic solutions?
what do you guys recommend ? also state the major difference of them... especially of bashing pros and cons..
2 replies
John_Mgr
2 hours ago
GreekIdiot
4 minutes ago
J
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Regarding Maaths olympiad prepration
omega2007   0
6 minutes ago
<Hey Everyone'>
I'm 10 grader student and Im starting prepration for maths olympiad..>>> From scratch (not 2+2=4 )

Do you haves compilled resources of Handouts,
PDF,
Links,
List of books topic wise
which are shared on AOPS (and from your prespective) for maths olympiad and any useful thing, which will help me in boosting Maths olympiad prepration.
0 replies
omega2007
6 minutes ago
0 replies
J
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Inspired by JK1603JK
sqing   13
N 14 minutes ago by sqing
Source: Own
Let $ a,b,c\geq 0 $ and $ab+bc+ca=1.$ Prove that$$\frac{abc-2}{abc-1}\ge \frac{4(a^2b+b^2c+c^2a)}{a^3b+b^3c+c^3a+1} $$
13 replies
+1 w
sqing
Today at 3:31 AM
sqing
14 minutes ago
J
No more topics!
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Perfect Numbers
steven_zhang123   1
N Mar 30, 2025 by lyllyl
Source: China TST 2001 Quiz 8 P2
If the sum of all positive divisors (including itself) of a positive integer $n$ is $2n$, then $n$ is called a perfect number. For example, the sum of the positive divisors of 6 is $1 + 2 + 3 + 6 = 2 \times 6$, hence 6 is a perfect number.
Prove: There does not exist a perfect number of the form $p^a q^b r^c$, where $a, b, c$ are positive integers, and $p, q, r$ are odd primes.
1 reply
steven_zhang123
Mar 30, 2025
lyllyl
Mar 30, 2025
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Perfect Numbers
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Reveal topic tags
China TST
number theory
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G H BBookmark kLocked kLocked NReply
Source: China TST 2001 Quiz 8 P2
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steven_zhang123
408 posts
steven_zhang123
#1 h  Mar 30, 2025, 12:09 AM
Y by
If the sum of all positive divisors (including itself) of a positive integer $n$ is $2n$, then $n$ is called a perfect number. For example, the sum of the positive divisors of 6 is $1 + 2 + 3 + 6 = 2 \times 6$, hence 6 is a perfect number.
Prove: There does not exist a perfect number of the form $p^a q^b r^c$, where $a, b, c$ are positive integers, and $p, q, r$ are odd primes.
Z K Y
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lyllyl
4 posts
lyllyl
#2 h  Mar 30, 2025, 3:25 AM
Y by
If not,assumn p<q<r, so 2p^a*q^b*r^c<p^(a+1)q^(b+1)r^(c+1)/(p-1)(q-1)(r-1),which tells us p=3 q=5 r=7,11,13,verify one by one.
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